Related papers: A Method of Solving Certain Nonlinear Diophantine …
We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation.…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method builds upon the formulation introduced in Bertalmio et al., J. Comput. Phys., 174 (2001),…
In this paper, we first show the existence of solutions to the following system of nonlinear equations \begin{eqnarray*}\left\{\begin{array}{l} a_{11}x_1+a_{12}x_2+a_{13}x_3+\cdots+a_{1n}x_{n} =…
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor networks, we provide new and improved results on the matter using…
In this paper, we solve the simultaneous Diophantine equations m.(x_1^k+....+x_{t_1}^k)=n.(y_1^k+....+y_{t_2}^k); k=1,3, where t_1, t_2>3, and m, n are fixed arbitrary and relatively prime positive integers. This is done by choosing two…
We present a new method for constructing solutions to nonlinear evolutionary equations describing the propagation and interaction of nonlinear waves.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
Recursive formulas are derived for the number of solutions of linear and quadratic Diophantine equations with positive coefficients. This result is further extended to general non-linear additive Diophantine equations. It is shown that all…
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…
We present a new view onto the successive approximations' approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel…
One of old methods for finding exact solutions of nonlinear differential equations is considered. Modifications of the method are discussed. Application of the method is illustrated for finding exact solutions of the Fisher equation and…
We give evaluations in closed form of certain non linear differential equations
We present some results in the analysis of non-compact differential equations on unbounded domains.